I counted and it took no less than 15 tries before it ever worked for me. Ever since then then my rates have improved but I'm still highly skeptical of the "1 in 4" written on the card.
The odds never stack, so it’s not like you are due a win just because there were so many “nope!”s. It’s always 1 in 4, which is 25% chance (0% in xcom terms).
I mean.. that's a pretty weird take. Most games have some sort of RNG - whether it be in the background or visibility listed probabilities. That doesn't mean they're promoting gambling.
The outrage over the 18+ rating was partially over other games with actual gambling (monetized loot boxes) are somehow PG / PG-13.
Meanwhile, this game with no in-game purchases and is only thematically about "Poker" is 18+ because it's "promoting gambling".. If the game had an artwork swap they'd see it as a typical deck building rougelite and rate it the same as Slay the Spire.